Question

Consider the following statement:

a) Resistivity of conductor increases as temperature increases

b) Resistivity of the conductor decreases as temperature increases

c) If the length of the wire increases, its resistivity also increases

Which of the above statement is/are correct:

1. Only a is correct
2. Only b is correct
3. Both a and c are correct
4. Both b and c are correct

Answer 1

Correct Answer - Option 1 : Only a is correct

CONCEPT:

Resistivity (ρ):

• The property of a conductor that opposes the flow of electric current through them and independent of the shape and size of the materials but depends on the nature and temperature of the materials is called resistivity.
  • The unit for resistivity is the ohm-meter (Ω-m).
  • The resistivity of a material depends on its nature and the temperature of the conductor.
  • The resistivity of a material doesn't depend on its shape and size (length and area).
  • The resistivity of the conductor increases as the temperature increases.

EXPLANATION:

• The resistivity of any material depends on the temperature as

⇒ ρ_t = ρ0 [1 + α (T - T0)]

where, ρ0 = resistivity at standard temperature, ρ_t = resistivity at temperature t0 C, T0 = reference temperature, α  = the temperature coefficient of resistivity.

• The resistivity of a material doesn't depend on its shape and size (length and area).
• The resistivity of the conductor increases as the temperature increases.
• So by the above explanation, we can say that only the statement a is correct.
• Hence, option 1 is correct.

Resistance is given as

\(R =\rho \frac{l}{A}\)

l is the length of the conductor, A is cross-sectional area.

It does not mean, resistivity depends on the resistance.

Resistance depends upon resistivity, but the opposite is not true.